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Question

Three vectors a,b,c are such that |a|=1,b=2,|c|=4 and a+b+c=0. Then the value of a.b+3b.c+3c.a is equal to :

A
68
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B
26
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C
34
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D
27
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Solution

The correct option is A 26
c=ab
4(ab)+3(b.c)+3(c.a)=4(a.b)+3b.(ab)+3(a.(ab
=4(a.b)3(a.b)=2|b|23|a|23(a.b)2(a.b)3(4)3(1)=152(a.b)
a+b=c
(a+b)=|c|
or 1+4+2(ab=4
2(a.b=11(a.b)=112
152(a.b)=1511=26

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